In cross-over trials, various types of responses may be recorded, not all of which can be appropriately modelled by a Normal distribution. Widening the class of models to the generalized linear model family has a number of advantages. An important one is that certain interactions, especially that between patients and treatments, can easily be fitted for frequency and count data. These can be used as diagnostics for the fit of the model used. One handicap has been the frequentist difficulty of comparing the fit of different non-nested models in this family. This can be overcome by the use of a model selection criterion such as the Akaike or Bayesian information criterion. This approach to modelling and diagnostics for cross-over trials is applied to two studies involving small counts of anginal attacks, previously analysed in the literature using classical Normal techniques.